$\text{a)}f\left(x\right)=\frac{1}{x}\stackrel{\overrightarrow{u}=\left[1,4\right]}{\to }g\left(x\right)=\frac{1}{x-1}+4$  

• $D_g=\mathbf{R}\backslash \left\{1\right\}$  
• $g\left(D_g\right)=\mathbf{R}\backslash \left\{4\right\}$  
• asymptota pozioma: y=4
• asymptota pionowa: x=1

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$\text{b)}f\left(x\right)=\frac{2}{x}\stackrel{\overrightarrow{u}=\left[-2,-1\right]}{\to }g\left(x\right)=\frac{2}{x+2}-1$  

• $D_g=\mathbf{R}\backslash \left\{-2\right\}$  
• $g\left(D_g\right)=\mathbf{R}\backslash \left\{-1\right\}$  
• asymptota pozioma: y=-1
• asymptota pionowa: x=-2

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$\text{c)}f\left(x\right)=-\frac{1}{x}\stackrel{\overrightarrow{u}=\left[-1,3\right]}{\to }g\left(x\right)=-\frac{1}{x+1}+3$  

• $D_g=\mathbf{R}\backslash \left\{-1\right\}$  
• $g\left(D_g\right)=\mathbf{R}\backslash \left\{3\right\}$  
• asymptota pozioma: y=3
• asymptota pionowa: x=-1

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$\text{d)}f\left(x\right)=-\frac{2}{x}\stackrel{\overrightarrow{u}=\left[2,-4\right]}{\to }g\left(x\right)=-\frac{2}{x-2}-4$  

• $D_g=\mathbf{R}\backslash \left\{2\right\}$  
• $g\left(D_g\right)=\mathbf{R}\backslash \left\{-4\right\}$  
• asymptota pozioma: y=-4
• asymptota pionowa: x=2